The fifth edition of this very successful book, based on the experience and notes of the authors while teaching mathematics courses to engineering students for more than three decades, emphasizes the fundamental and theoretical concepts. The key features of the book are illustrative examples and exercises that explain each theoretical concept. NEW TO THE FIFTH EDITION: • In Chapter 3, a new section 3.9: More on Vector Spaces has been included. This section deals with Sum of Subspaces, Direct Sum of Subspaces, complimentary subspaces and Inner Product Spaces, and Gram-Schmidt Orthogonalization Process. • Editing and minor additions to the Chapters have been done based on the suggestions of the readers. Functions of a Real Variable Functions of Several Real Variables Matrices and Eigenvalue Problems Ordinary Differential Equations of First Order Linear Differential Equations Series Solution of Differential Equation Legendre Polynomials, Chebysher Polynomials, Bessel Functions and Sturm-Liouvelle Problem Laplace Transformation Fourier Series, Fourier Integrals and Fourier Transform Functions of a Complex Variables: Analytic Functions Integration of Complex Functions Power Series, Taylor and Laurent Series Zeros, Singularities and Residues Billinear Transformation and Conformal Mapping Vector Differential and Integral Calculus Partial Differential Equations Z Transformation Numerical Methods Theory of Probability Mathematical Statistics – Tests of Significance